The article presents the concept of creating model of delays occurring in telecommunication system taking into account all sources of delays generated during data transmission between the source and destination nodes. Proposed model takes into account the existence of intermediary network devices that play a significant role in the general delay budget. The paper presents two measurement systems used to measure delays in 802.11 g based wireless networks and ones using ZigBee standard. Both systems were built based on the authors' concepts of hardware and software allowing measurement of delays by using additional connection for the synchronization of internal clocks. Described measurement systems selected amount of experiments was performed for varied network structures.